https://doi.org/10.1140/epjb/s10051-025-00988-1
Research – Statistical and Nonlinear Physics
Correlation time in extremal self-organized critical models
Department of Physics, Institute of Science, Banaras Hindu University, 221005, Varanasi, Uttar Pradesh, India
Received:
10
January
2025
Accepted:
14
June
2025
Published online:
26
June
2025
We investigate correlation time numerically in extremal self-organized critical models, namely the Bak–Sneppen evolution and the Robin Hood dynamics. The (fitness) correlation time is the duration required for the extinction or mutation of species over the entire spatial region in the critical state. We apply the methods of finite-size scaling and extreme value theory to understand the statistics of the correlation time. We find power-law system size scaling behaviors for the mean, the variance, the mode, and the peak probability of the correlation time. We obtain data collapse for the correlation time cumulative probability distribution, and the scaling function follows the generalized extreme value density close to the Gumbel function.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
